Decomposition Algorithm for Optimization Placement Problems - Pankratov, A.; Romanova, T. (Математичне та комп'ютерне моделювання. Серія: Технічні науки, 2019)
The paper considers a placement problem of 2D convex objects in a rectangular domain of minimum area, that related to the field of Packing and Cutting problems. Our objects may be continuously translated and rotated. A nonlinear programming model of the problem is derived using the phi-function technique. We develop an efficient decomposition algorithm to search for local optimal solutions for the placement problem. The algorithm reduces our problem to a sequence of nonlinear programming subproblems of considerably smaller dimension and a smaller number of nonlinear inequalities. The benefit of this approach is borne out by the computational results.